Handbook of Modeling High-Frequency Data in

Written and edited by leading, international experts in the field, Handbook of Modeling High-Frequency Data in Finance presents cutting-edge developments in high frequency financial econometrics, spanning a diverse range of topics: stochastic modeling, statistical analysis of high-frequency data, models in econophysics, applications to the analysis of high-frequency data, and systems and complex adaptive systems in finance, among others. By using examples derived from consulting projects, current research, and course instruction, each chapter offers practitioners a systematic understanding of the recent advances in high-frequency modeling related to real-world situations.

Frederi G. Viens, PhD, is Director and Coordinator of the Computational Finance Program at Purdue University, where he also serves as Professor of Statistics and Mathematics. He has published extensively in the areas of mathematical finance, probability theory, and stochastic processes. Dr. Viens is co-organizer of the annual Conference on Modeling High-Frequency Data in Finance. Maria C. Mariani, PhD, is Professor and Chair in the Department of Mathematical Sciences at The University of Texas at El Paso. She currently focuses her research on mathematical finance, applied mathematics, and numerical methods. Dr. Mariani is co-organizer of the annual Conference on Modeling High-Frequency Data in Finance. Ionut Florescu, PhD, is Assistant Professor of Mathematics at Stevens Institute of Technology. He has published in research areas including stochastic volatility, stochastic partial differential equations, Monte Carlo methods, and numerical methods for stochastic processes. Dr. Florescu is lead organizer of the annual Conference on Modeling High-Frequency Data in Finance.

Preface	p. xi
Contributors	p. xiii
Analysis of Empirical Data	p. 1
Estimation of Nig and Vg models for High Frequency Financial Data	p. 3
Introduction	p. 3
The Statistical Models	p. 6
Parametric Estimation Methods	p. 9
Finite-Sample Performance via Simulations	p. 14
Empirical Results	p. 18
Conclusion	p. 22
References	p. 24
A Study of Persistence of Price Movement using High Frequency Financial Data	p. 27
Introduction	p. 27
Methodology	p. 29
Results	p. 35
Rare Events Distribution	p. 41
Conclusions	p. 44
	p. 45
Using Boosting for Financial Analysis and Trading	p. 47
Introduction	p. 47
Methods	p. 48
Performance Evaluation	p. 53
Earnings Prediction and Algorithmic Trading	p. 60
Final Comments and Conclusions	p. 66
References	p. 69
Impact of Correlation Fluctuations on Securitized Structures	p. 75
Introduction	p. 75
Description of the Products and Models	p. 77
Impact of Dynamics of Default Correlation on Low-Frequency Tranches	p. 79
Impact of Dynamics of Default Correlation on High-Frequency Tranches	p. 87
Conclusion	p. 92
References	p. 94
Construction of Volatility Indices Using a Multinomial Tree Approximation Method	p. 97
Introduction	p. 97
New Methodology	p. 99
Results and Discussions	p. 101
Summary and Conclusion	p. 110
References	p. 115
Long Range Dependence Models	p. 117
Long Correlations Applied to the Study of Memory Effects in High Frequency (TICK) Data, the Dow Jones Index, and International Indices	p. 119
Introduction	p. 119
Methods Used for Data Analysis	p. 122
Data	p. 128
Results and Discussions	p. 132
Conclusion	p. 150
References	p. 160
Risk Forecasting with GARCH, Skewed t Distributions, and Multiple Timescales	p. 163
Introduction	p. 163
The Skewed t Distributions	p. 165
Risk Forecasts on a Fixed Timescale	p. 176
Multiple Timescale Forecasts	p. 185
Backtesting	p. 188
Further Analysis: Long-Term GARCH and Comparisons using Simulated Data	p. 203
Conclusion	p. 216
References	p. 217
Parameter Estimation and Calibration for Long-Memory Stochastic Volatility Models	p. 219
Introduction	p. 219
Statistical Inference Under the LMSV Model	p. 222
Simulation Results	p. 227
Application to the S&P Index	p. 228
Conclusion	p. 229
References	p. 230
Analytical Results	p. 233
A Market Microstructure Model of Ultra High Frequency Trading	p. 235
Introduction	p. 235
Microstmctural Model	p. 237
Static Comparisons	p. 239
Questions for Future Research	p. 241
References	p. 242
Multivariate Volatility Estimation with High Frequency Data Using Fourier Method	p. 243
Introduction	p. 243
Fourier Estimator of Multivariate Spot Volatility	p. 246
Fourier Estimator of Integrated Volatility in the Presence of Microstructure Noise	p. 252
Fourier Estimator of Integrated Covariance in the Presence of Microstructure Noise	p. 263
Forecasting Properties of Fourier Estimator	p. 272
Application: Asset Allocation	p. 286
References	p. 290
The "Retirement" Problem	p. 295
Introduction	p. 295
The Market Model	p. 296
Portfolio and Wealth Processes	p. 297
Utility Function	p. 299
The Optimization Problem in the Case ¿_{¿, T} = 0	p. 299
Duality Approach	p. 300
Infinite Horizon Case	p. 305
References	p. 324
Stochastic Differential Equations and Levy Models with Applications to High Frequency Data	p. 327
Solutions to Stochastic Differential Equations	p. 327
Stable Distributions	p. 334
The Levy Flight Models	p. 336
Numerical Simulations and Levy Models: Applications to Models Arising in Financial Indices and High Frequency Data	p. 340
Discussion and Conclusions	p. 345
References	p. 346
Solutions to Integro-Differential Parabolic Problem Arising on Financial Mathematics	p. 347
Introduction	p. 347
Method of Upper and Lower Solutions	p. 351
Another Iterative Method	p. 364
Integro-Differential Equations in a Lévy Market	p. 375
References	p. 380
Existence of Solutions for Financial Models with Transaction Costs and Stochastic Volatility	p. 383
Model with Transaction Costs	p. 383
Review of Functional Analysis	p. 386
Solution of the Problem (14.2) and (14.3) in Sobolev Spaces	p. 391
Model with Transaction Costs and Stochastic Volatility	p. 400
The Analysis of the Resulting Partial Differential Equation	p. 408
References	p. 418
Index	p. 421
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Handbook of Modeling High-Frequency Data in Finance

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